Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives

This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation...

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Bibliographic Details
Main Author: Ricardo Almeida
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Fractal and Fractional
Subjects:
Online Access:https://www.mdpi.com/2504-3110/9/3/188
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Summary:This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation for this generalized case and providing optimality conditions for extremal curves. We explore problems with integral and holonomic constraints and consider higher-order derivatives, where the fractional orders are free.
ISSN:2504-3110